Preserving Steady-State in One-Dimensional Finite-Volume Computations of River Flow
Publication: Journal of Hydraulic Engineering
Volume 134, Issue 9
Abstract
When using finite-volume methods and the conservative form of the Saint Venant equations in one-dimensional flow computations, it is important to establish the correct balance between the discretized flux vector and the geometric source terms. Over the last few years various improvements to numerical schemes have been presented to achieve this correct balance, focusing on the capability to simulate water at rest on irregular geometries (C-property). In this paper it is shown that common schemes can lead to energy-violating solutions in the case of steady flow. We present developments based on the Roe TVD finite-volume scheme for one-dimensional Saint Venant equations, which results in a method that not only satisfies the C-property, but also preserves the correct steady flow when stationary boundary conditions are used. We also present a totally irregular channel test case for the verification of the method.
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References
Alcrudo, F. (1992). “Esquemas de alta resolución de variación total decreciente para el estudio de flujos discontinuos de superficie libre.” Ph.D. thesis, Facultad de Ciencias. Universidad de Zaragoza, Zaragoza, Spain.
Bladé, E., and Gómez-Valentín, M. (2006). “Modelación del flujo en lámina libre sobre cauces naturales. Análisis integrado en una y dos dimensiones.” Monograph CIMNE No. 97, Barcelona, Spain.
Burguete, J., and García-Navarro, P. (2004). “Improving simple explicit methods for unsteady open channel and river flow.” Int. J. Numer. Methods Fluids, 45, 125–156.
Cunge, J. A., Holly, Jr., F. M., and Verwey, A. (1980). “Practical aspects of computational river hydraulics.” Pitman, London.
Hubbard, M. E. and García-Navarro, P. (2000). “Flux difference splitting and the balancing of source terms and flux gradients.” J. Comput. Phys., 165, 89–125.
Sanders, B. F., Jaffe, A., and Chu, A. K. (2003). “Discretization of integral equations describing flow in nonprismatic channels with uneven beds.” J. Hydrol. Eng., 129(3), 235–244.
Toro, E. F. (1997). “Riemann solvers and numerical methods for fluid dynamics. A practical introduction.” Springer, Berlin Heidelberg.
Tseng, M.-H. (2004). “Improved treatment of source terms in TVD scheme for shallow water equations.” Adv. Water Resour., 27, 617–629.
Vázquez-Cendón, M. E. (1999). “Improved treatment of source terms in upwind schemes for the shallow water equations in channels with irregular geometry.” J. Comput. Phys., 148, 497–526.
Vukovic, S. and Sopta, L. (2003). “Upwind schemes with exact conservation property for one-dimensional open channel flow equations.” SIAM J. Sci. Comput. (USA), 24(5), 1630–1649.
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Information
Published In
Journal of Hydraulic Engineering
Volume 134 • Issue 9 • September 2008
Pages: 1343 - 1347
Copyright
© 2008 ASCE.
History
Received: May 15, 2007
Accepted: Dec 18, 2007
Published online: Sep 1, 2008
Published in print: Sep 2008
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